{"paper":{"title":"On the odd girth and the circular chromatic number of generalized Petersen graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Amir Daneshgar, Meysam Madani","submitted_at":"2015-01-26T20:34:37Z","abstract_excerpt":"A class of simple graphs such as ${\\cal G}$ is said to be {\\it odd-girth-closed} if for any positive integer $g$ there exists a graph $G \\in {\\cal G}$ such that the odd-girth of $G$ is greater than or equal to $g$. An odd-girth-closed class of graphs ${\\cal G}$ is said to be {\\it odd-pentagonal} if there exists a positive integer $g^*$ depending on ${\\cal G}$ such that any graph $G \\in {\\cal G}$ whose odd-girth is greater than $g^*$ admits a homomorphism to the five cycle (i.e. is $C_{_{5}}$-colorable).\n  In this article, we show that finding the odd girth of generalized Petersen graphs can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06551","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}